1,861 research outputs found
Phase Diagrams of Bi1-xSbx Thin Films with Different Growth Orientations
A closed-form model is developed to evaluate the band-edge shift caused by
quantum confinement for a two-dimensional non-parabolic carrier-pocket. Based
on this model, the symmetries and the band-shifts of different carrier-pockets
are evaluated for BiSb thin films that are grown along different crystalline
axes. The phase diagrams for the BiSb thin film systems with different growth
orientations are calculated and analyzed
Graphon Control of Large-scale Networks of Linear Systems
To achieve control objectives for extremely large-scale complex networks
using standard methods is essentially intractable. In this work a theory of the
approximate control of complex network systems is proposed and developed by the
use of graphon theory and the theory of infinite dimensional systems. First,
graphon dynamical system models are formulated in an appropriate infinite
dimensional space in order to represent arbitrary-size networks of linear
dynamical systems, and to define the convergence of sequences of network
systems with limits in the space. Exact controllability and approximate
controllability of graphon dynamical systems are then investigated. Second, the
minimum energy state-to-state control problem and the linear quadratic
regulator problem for systems on complex networks are considered. The control
problem for graphon limit systems is solved in each case and approximations are
defined which yield control laws for the original control problems.
Furthermore, convergence properties of the approximation schemes are
established. A systematic control design methodology is developed within this
framework. Finally, numerical examples of networks with randomly sampled
weightings are presented to illustrate the effectiveness of the graphon control
methodology.Comment: 16 pages. To appear in the IEEE Transactions on Automatic Control,
2020. Originally announced July 201
Spectral Representations of Graphons in Very Large Network Systems Control
Graphon-based control has recently been proposed and developed to solve
control problems for dynamical systems on networks which are very large or
growing without bound (see Gao and Caines, CDC 2017, CDC 2018). In this paper,
spectral representations, eigenfunctions and approximations of graphons, and
their applications to graphon-based control are studied. First, spectral
properties of graphons are presented and then approximations based on Fourier
approximated eigenfunctions are analyzed. Within this framework, two classes of
graphons with simple spectral representations are given. Applications to
graphon-based control analysis are next presented; in particular, the
controllability of systems distributed over very large networks is expressed in
terms of the properties of the corresponding graphon dynamical systems.
Moreover, spectral analysis based upon real-world network data is presented,
which demonstrates that low-dimensional spectral approximations of networks are
possible. Finally, an initial, exploratory investigation of the utility of the
spectral analysis methodology in graphon systems control to study the control
of epidemic spread is presented.Comment: 8 pages, 58th IEEE Conference on Decision and Control (CDC 2019
Landau-Zener-St\"uckelberg Spectroscopy of a Superconducting Flux Qubit
We proposed a new method to measure the energy spectrum of a superconducting
flux qubit. Different from the conventional frequency spectroscopy, a short
triangle pulse is used to drive the qubit through the anticrossing and
generates Landau-Zener-St\"uckelberg interference patterns, from which the
information of the energy spectrum can be extracted. Without installing
microwave lines one can simplify the experimental setup and reduce the unwanted
effects of noise. Moreover, the method can be applied to other quantum systems,
opening the possibility of calibrating and manipulating qubits with linear
pulses.Comment: 7 pages, 5 figure
Dilaton Black Holes in de Sitter or Anti-de Sitter Universe
Poletti and Wiltshire have shown that, with the exception of a pure
cosmological constant, the solution of a dilaton black hole in the background
of de Sitter or anti-de Sitter universe, does not exist in the presence of one
Liouville-type dilaton potential. Here with the combination of three
Liouville-type dilaton potentials, we obtain the dilaton black hole solutions
in the background of de Sitter or anti-de Sitter universe.Comment: 13 pages,to appear in Phys. Rev.
Age Problem in the Holographic Dark Energy Model
In this note, we test the original holographic dark energy model with some
old high redshift objects. The main idea is very simple: the universe cannot be
younger than its constituents. We find that the original holographic dark
energy model can be ruled out, unless a lower Hubble constant is taken.Comment: 12 pages, 3 tables, 3 figures, revtex4; v2: accepted for publication
in Phys. Rev. D; v3: published versio
Linear Quadratic Graphon Field Games
Linear quadratic graphon field games (LQ-GFGs) are defined to be LQ games
which involve a large number of agents that are weakly coupled via a weighted
undirected graph on which each node represents an agent. The links of the graph
correspond to couplings between the agents' dynamics, as well as between the
individual cost functions, which each agent attempts to minimize. We formulate
limit LQ-GFG problems based on the assumption that these graphs lie in a
sequence which converges to a limit graphon. First, under a finite-rank
assumption on the limit graphon, the existence and uniqueness of solutions to
the formulated limit LQ-GFG problem is established. Second, based upon the
solutions to the limit LQ-GFG problem, epsilon-Nash equilibria are constructed
for the corresponding game problems with a very large but finite number of
players. This result is then generalized to the case with random initial
conditions. It is to be noted that LQ-GFG problems are distinct from the class
of graphon mean field game (GMFG) problems where a population is hypothesized
to be associated with each node of the graph [Caines and Huang CDC 2018, 2019]
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